Air New Zealand said aircraft were departing, but arrivals were impacted by low visibility.
Four flights into Christchurch had diverted or returned to their departure port, a spokesperson said, and three flights had been delayed.
"As a result, seven flights in and out of Christchurch have been cancelled."
Air New Zealand was monitoring conditions and working to rebook impacted customers on the next available service, the spokesperson said.
"We recommend customers travelling from Christchurch today keep an eye on the Air NZ app and the arrivals and departures page on our website for the latest flight updates."
There were no significant weather-related disruptions outside of Christchurch, Air New Zealand said.
Christchurch Airport's arrivals and departures page showed flights into Christchurch from Auckland, Palmerston North, Napier and Queenstown had been cancelled, while flights from Wellington and Auckland had been delayed, as of 9.45am Saturday.
Flights out of Christchurch to Napier and Rotorua had also been cancelled, while flights to Wānaka and Auckland were delayed.
Meanwhile, heavy rain is pounding parts of the North Island, with weather watches in place for Northland, Auckland, Coromandel Peninsula, Waikato and Waitomo until 8pm Saturday.
MetService told people to expect possible downpours and thunderstorms.
The amount of rain "may approach warning criteria and may even exceed warning amounts in localised areas", the forecaster said.
A heavy rain watch was also in place for Taupō and Bay of Plenty, including Rotorua, until 11pm Saturday.
